I have to say, though, that such a sentence ("I've made a brief or wrap-up of the conversation") isn't very clear in (American) English, at least not to my ear.

To make a "brief" of a conversation is idiomatic if you are a lawyer (or playing on that language), yet such "briefs" are usually made "for" a conversation (that is, in the future).

Making a "wrap-up" of a conversation is really something you do to "end" the conversation within the conversation. Thus, this usage in the past-perfective doesn't make a lot of sense.

The common-use for "synthesis" in this case would be "summary," that is:

I have made a summary of the conversation.

I realize that the word summary does not seem to imply the act of synthesizing the content of conversation. Nevertheless, "summary" does carry that connotation in this context.

To be more technical, you could draw out the (formally speaking) synthetic quality of the summary by saying something like:

I have distilled the content of the conversation in a brief summary.

The word "summation" is also common-use for this context and is slightly more formal than "summary." To split the difference between the "distillation" sentence and the "summary" sentence, you could say:

I have made a summation of the conversation

or even

I have made a [short/brief/concise...pick your adjective] summation of the conversation.

A further note: When I taught English composition at the university a decade ago, we routinely referred to the skill of summarization as "synthesis." We used the term "synthesis papers" to refer to what students would normally call "summaries." We did so, I think, to attempt to draw more critical attention to a basic process that most students take for granted.

Commonly, however, the term "synthesis" is not used in (American) English to convey this meaning. For the most part, synthesis is something that happens in a laboratory. The term "distill," however, is very much common and idiomatic and can be used interchangeably with the phrase "boiling down," as in:

"Calvin, young lad, can you boil this conversation down for me, I mean distill it into a really short summary that I can present to the board of directors on Friday?"

To which Calvin might reply: "Yes, boss, of course. I'll write up a brief for you, so that you don't miss a thing."

Now, in reality, legal briefs are often anything but "brief." Nevertheless, this last sentence is idiomatic to common use in formal or semi-formal situations, especially, as illustrated in the example, when "speaking up" or intentionally trying to elevate the conversation. Take for example, this next sentence overheard in the break room:

"Calvin, I heard you have to write up a brief for the boss."

"Yes, but it's not as complicated as you make it sound. He just wants me to get him a summary of the conversation we had this morning so that he doesn't forget anything when he talks to the board."